# Document

```Chapter 10 Enzyme Kinetics

2011.10.11
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

① Elementary reaction and Stoichiometric equation

②Kinetic equation

③Rate limiting step

④Molecularity and order of reaction

① First-order reaction
v = k[S], k means rate constant (速率常数)
[S] = [S0]e-kt
half-life: t1/2=0.6931/k
② Second-order reaction
v = k[SA][SB], if [SA] = [SB], v = k[S]2
t1/2=1/k[S]
③ Zero-order reaction
v=k
t1/2=[S]/2k

V0: initial rate
Vmax: maximum veloxity
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① 单底物、单产物反应；
② 酶促反应速率一般在规定的反应条件下，用

③ 反应速率取其初速率，即底物的消耗量很小
（一般在5﹪以内）时的反应速率
④ 底物浓度远远大于酶浓度。
Michaelis-Menten Model
Ks = k1/k-1
k-2 is ignored if P is negligible at initial stage
rate limiting step
fast reversible step
[E] = [Et] – [ES]
[S] &gt;&gt; [Et], [S] unchanged
=
Km = (k2 + k-1)/k1
[S]高，致使酶分子都被饱和，反应达到最大速度，则：
[ES] = [Et]
Vmax = k2[ES] = k2 [Et]
Michaelis-Menten equation
[S]：底物浓度
V0：不同[S]时的初始反应速率
Vmax：最大反应初速率 Ｋm：米氏常数
Km值等于酶促反应速率为最大反应速率一半时的底物

Km的意义：
 Km是酶的特征性常数之一，只与酶的结构、底物和

 Km可近似表示酶对底物的亲和力
 同一酶对于不同底物有不同的Km值
Vmax的意义
 定义：Vmax是酶完全被底物饱和时的反应初速

意义：Vmax=k2 [Et]

specificity constant

E+ S
E+P
kcat/Km: apparent second-order constant

kcat/Km = k1

catalytic perfection (催化活性的完美程度)
Km &gt;&gt; [S]
[S] &gt;&gt; Km
V
Vmax
[S]
当底物浓度较低时：

V
Vmax
[S]
随着底物浓度的增高：

V
Vmax
[S]
当底物浓度高达一定程度：

Transformation of the Michaelis-Menten equation into
double-reciprocal plot (双倒数作图）
Lineweaver-Burk equation
is rate-limiting (for most enzymes)
Vmax = k3[Et]
If the reaction has several steps and one is clearly ratelimiting, kcat is equivalent to the rate constant for that
limiting step; when several steps are partially ratelimiting, kcat = f (kcat1, kcat2,…. kcatn )
Enzymatic Reactions with Two or More Substrates
1.Many of the principles developed for the single-substrate systems
may be extended to multisubstrate systems.
2.The majority of enzymes involve two substrates.
3.Most reactions obey Michaelis-Menten kinetics when the
concentration of one substrate is held constant and the other is varied.
Enzymatic reactions with two substrates usually involve
transfer of an atom or a functional group from one
substrate to the other:
 Sequential mechanism （顺序反应机制）
Sequential mechanism
Steady-state kinetic analysis of bisubstrate reactions
double-reciprocal plot when [S1] fixed and [S2] varied,
generating several intersecting lines,indicating that a
ternary complex is formed in the reaction.
Ping-pong mechanism （乒乓机制）
Enzyme activity is affected by pH and temperature
1. Each enzyme has an optimal pH or pH range（最适pH)
(where the enzyme has maximal activity).
① Requirements for the catalytic groups in the active
site in appropriate ionization state is a common
reason for this phenomenon.

② Change of ionization state of surface groups (which
may affect the protein structure) sometimes is
responsible for this phenomenon.

③ In rare cases, it is the change of ionization state of
substrate that is responsible for this phenomenon.

2. Each enzyme has an optimal temperature or
temperature range（最适温度) (where the enzyme has
maximal activity).
① Requirements for the appropriate conformation of
the enzyme

② At low temperature, thermal motion (热运动) of
molecules is low, and thus reaction rate is low.
(That’s why bilogical samples are usually kept in
fridge!) Within certain temperature range, the
activity increases with the temperature until the
maximal activity is reached (at optimum
temperature).
③ At higher temperatures, enzymes will denature (变

activity.
Enzymes are subject to reversible and
irreversible inhibition




 抑制剂对酶有一定选择性，涉及酶的

 引起变性的因素对酶没有选择性，涉

 抑制作用的类型

 不可逆性抑制 (irreversible inhibition)
 可逆性抑制 (reversible inhibition)
竞争性抑制 (competitive inhibition)
非竞争性抑制 (non-competitive inhibition)
反竞争性抑制 (uncompetitive inhibition)
 Reversible inhibitors : bind to enzyme non-covalently
① Competitive inhibitor competes with the substrate for
the active site of an enzyme (binding of one prevents
binding of the other, forming ES or EI complexes but no
ESI complexes; of course, EI can not give off normal
products! ). Competitive inhibitors are often compounds
that resemble the substrates.
Transition state analogs（过渡态类似物）act as potent
inhibitors for enzymes.
k1
k2
ki1
ki2
k2+k3
Km =
k1
ki2
Ki =
=
ki1
k3
1/V

1/[S]
抑制程度取决于抑制剂与酶的相对亲和力及底物浓

动力学特点：Vmax不变，表观Km增大。
Biochemistry in Life
磺胺类药物的抑菌机制
——与对氨基苯甲酸竞争二氢叶酸合成酶

H 2N
COOH
H2N
SO2NHR

Biochemistry in Life
Methanol (甲醇）ingestion
alcohol dehydrogenase
In liver
Formaldehyde (甲醛）
ethanol
acetaldehyde
Blindness
② Noncompetitive inhibitor (非竞争性抑制）binds
at a site distinct from the substrate active site, and it
binds to either E or ES.
1/V

1/[S]
抑制程度取决于抑制剂的浓度；
动力学特点：Vmax降低，表观Km不变。
Mixed inhibitor (混合型抑制）can form the
complex EI with E, and affects the binding between
E and S.
动力学特点：Vmax降低，表观Km增大。
③ Uncompetitive inhibitor (非竞争性抑制）binds at
a site distinct from the substrate active site and only
to the ES complex, but is unable to bind free E.
•
1/V

1/[S]
抑制程度取决与抑制剂的浓度及底物的浓度；
动力学特点：Vmax和表观Km降低相同的倍数。

E
Km
Vmax
Km/Vmax
1/Vmax
-1/Km

E、ES
ES

 Inreversible inhibitors (不可逆抑制剂）: bind very
tightly (covalently or noncovalently) to the enzymes, and
destroy the catalytic activity.
chymotrypsin
(异丙基氟磷酸)
Suicide inhibitors (自杀性抑制剂）: bind to the active
site of a specific enzyme, then undergo a few chemical
steps of normal reactions, but instead of being transformed
into the normal products, they are converted into a very
reactive compound that combines irreversible with the
enzymes. They are called mechanism-based inactivators.
Biochemistry in Life
Curing African Sleeping Sickness with
a Biochemical Trojan Horse
Trypanosomes
(锥虫)
Ornithine decarboxylase
```